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4 years ago

Show that A x B does not equal B x A, when A and B are nonempty unless A=B.

1 answer:

8 0

We will assume A×B = B×A and show that A and B are necessarily the same.

Assume A×B = B×A. Let a ∈ A and b ∈ B. Then (a,b) ∈ A×B. Since A×B = B×A, we have (a,b) ∈ B×A. That is, a ∈ B and b ∈ A. Therefore, a ∈ A implies a ∈ B and b ∈ B implies b ∈ A. So A = B, as we had set out to do.

You might be interested in

Determine whether each expression is equivalent to x3−25x. Select Yes or No for each expression.

dem82 [27]

Answer:

I’m so sure, but I’ll try.

1. Yes

2. No

3. No

4. Yes

5. No

5 0

3 years ago

Solve. 20/n+10 = 10/n+20 n = -10 n = -20 n = 30 n = -30

kirill115 [55]

Answer:

20/n+10 = 10/n+20 n

multiply both side n,

n (20/n+10) = n(10/n+20 n)

20+10n = 10+20n^2

20+10n -20 = 10+20n^2 -20

10n = 20n^2 -10

10n - 10n = 20n^2 -10 -10n

0 = = 20n^2 -10 -10n

20n^2 -10 -10n = 0

n = 1 or n = -0.5

Step-by-step explanation:

5 0

3 years ago

On the first math test, Keiko answered 19 out of 25 questions correctly. On the

m_a_m_a [10]

Answer:

Keiko got a better answer on the test on her second test, and you could compare these two ratios as they are written.

Step-by-step explanation:

First: Convert each of the scores into percentages:

How do you convert ratios to percentages? Well, first we have to convert the ratio to a decimal or a fraction. Let's convert it to a fraction. So, 19 out of 25 will become $\frac{19}{25}$ , and 17 out of 20 will become $\frac{17}{20}$ . To convert a fraction to a percentage:

Divide the numerator by the denominator:

19 ÷ 25 = 0.76 AND 17 ÷ 20 = 0.85

Multiply your quotient by 100

0.76 x 100 = 76 AND 0.85 x 100 = 85

Add the percent sign

76% AND 85%

Now the two quantities are easier to compare. We can obviously see that 85% is bigger [and better] than 76%. So, the ratio that equals 85% - 17 out of 20 - is a better grade.

The second question was: Can you compare these two ratios as they are written? Explain why or why not.

Yes, you can compare these two ratios, just find the [positive] difference between the amount that she scored and the total number of scores that could be gained.

25 - 19 = 6

20 - 17 = 3

Since the equation with 20 and 17 in it has a smaller difference, it is most likely to have a greater value [because that means that Keiko got more right and less wrong, which means a greater mark which is also a greater quantity].

Thanks,

Topic: Quantity Relationships, Quantity Conversions

4 0

3 years ago

How do you simplify ratios

VladimirAG [237]

Answer: Simplifying ratios is just like simplifying fractions. Think of ratios as fractions. You divide a number that both numerator and denominator can be divided by.

Example

5/10 = 1/2

How did we get 1/2? Simple! You divide the numerator and denominator by 5.

5/10÷5/5=1/2

You do the same for ratios but the only difference is instead of putting a fraction bar (/) you put a colon (:)

Let's try another example but with a ratio!

Example

5:10 = 1:2

How did we get 1:2? Simple! Again we divided by 5 just like we did with the fraction example! So really ratios are just like fractions!

5:10÷5:5=1:2

Remember

The fraction bar is /

The ratio bar is :

Ratios are just like fractions but the symbol can sometimes trick people.

3 0

3 years ago

Suppose f(x) = 5x^2 + 7x...Find (-3)

ziro4ka [17]

Answer: F(x)=24

Step-by-step explanation:

f(x)=5(-3)^2+7(-3)

f(x)= 5(9)+7(-3)

f(x)=45-21

f(x)=24

7 0

3 years ago